[試題] 992 陸行老師 微積分 隨堂考
課程名稱：微積分
開課教師：陸行教授
開課系級：金融一
考試日期(年月日)：2011/5/11
考試時限(Mins)：60(mins)
試題本文：
1.Use the integral test to determine whether the given series converges or
diverges.(13 points)
∞
Σ(2/3k+1)
k=1
2.Use the p-series test to determine whether the given series converges or
diverges.(13 points)
∞
Σ(1/k^2.5)
k=1
3.Use the ratio test to determine whether the given series converges or
diverges.(13 points)
∞
Σ(2^k/k!)
k=1
4.Determine whether the given geometric series converges, and if so, find its
sum.
(a)(13 points)
∞
Σ(e^-0.2n)
n=1
(b)(13 points)
∞
Σ(-1)^n*2^n+1/3^n-3
n=2
5.Determine the radius of convergence and the interval of absolute convergence
for the given power series.(13 points)
∞
Σ(2^2k*x^k/k^2)
k=1
6.Find a power series for the given function and determine its interval of
absolute convergence.(13 points)
f(x)=1/2-x
7.Find the Taylor series for the given function at the indicated point a=0
(13 points).
f(x)=e^3x
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